Questions: Salamancas Enterprises' noncallable bonds currently sell for 1,120. They have a 15-year maturity, an annual coupon of 85, and a par value of 1,000. What is their yield to maturity? a. 5.84% b. 6.15% c. 6.47% d. 7.17%

Solution Steps

To find the yield to maturity (YTM) of a bond, we need to solve for the interest rate that equates the present value of the bond's future cash flows (coupon payments and par value at maturity) to its current market price. This involves using the formula for the present value of an annuity (for the coupon payments) and the present value of a lump sum (for the par value). The YTM is the rate \( r \) that satisfies the equation:

\[ P = \sum_{t=1}^{n} \frac{C}{(1+r)^t} + \frac{F}{(1+r)^n} \]

where:

• \( P \) is the current price of the bond (\$1,120),
• \( C \) is the annual coupon payment (\$85),
• \( F \) is the face value of the bond (\$1,000),
• \( n \) is the number of years to maturity (15),
• \( r \) is the yield to maturity.

This equation is typically solved using numerical methods, such as the Newton-Raphson method or a root-finding algorithm, since it cannot be solved algebraically.

We are given the following values for the bond:

• Current price \( P = 1120 \)
• Annual coupon payment \( C = 85 \)
• Face value \( F = 1000 \)
• Number of years to maturity \( n = 15 \)

The yield to maturity (YTM) is the rate \( r \) that satisfies the equation:

\[ P = \sum_{t=1}^{n} \frac{C}{(1+r)^t} + \frac{F}{(1+r)^n} \]

This can be rewritten as:

\[ 1120 = \sum_{t=1}^{15} \frac{85}{(1+r)^t} + \frac{1000}{(1+r)^{15}} \]

Using numerical methods, we find that the yield to maturity \( r \) is approximately:

\[ r \approx 0.0717 \]

To express the yield to maturity as a percentage, we multiply by 100:

\[ \text{YTM} \approx 0.0717 \times 100 = 7.1684\% \]

Final Answer